An adaptive scheme for quantum state tomography

The process of inferring and reconstructing the state of a quantum system from the results of measurements, better known as quantum state tomography, constitutes a crucial task in the emerging field of quantum technologies. Today it is possible to experimentally control quantum systems containing tens of entangled qubits and perform measurements of arbitrary observables with great accuracy. However, in order to complete characterize an unknown $n$-qubit state, quantum state tomography requires a number of measurements which grows exponentially with $n$. A possible way to avoid this problem consists in performing an incomplete tomographic procedure able to provide a good estimate of the true state with few measurements. This thesis proposes a scheme for $n$-qubit state tomography which aims to improve the fidelity between the reconstructed state and the target state. In particular, the scheme identifies the next measurement to perform based on the knowledge already acquired from the previous measurements on the experimental prepared state. The performance of this scheme was finally analyzed by means of simulations of quantum state tomography with product measurements as well as with entangled measurements. In both cases one observes that the here proposed adaptive scheme significantly outperforms a standard scheme in terms of the fidelity of the reconstructed state.